A 10 kg mass has kinetic energy of 5kJ. What is its velocity?

The kinetic energy (\(KE\)) of an object is related to its mass and velocity by the following equation:

\[
KE = \frac{1}{2} m v^2
\]

Where:
- \(KE\) is the kinetic energy,
- \(m\) is the mass,
- \(v\) is the velocity.

Given:
- \(KE = 5000 \, \text{J}\) (since 5 kJ = 5000 J),
- \(m = 10 \, \text{kg}\).

We can solve for \(v\) (velocity):

\[
5000 = \frac{1}{2} \times 10 \times v^2
\]

Now, solving for \(v\):

\[
5000 = 5 \times v^2
\]

\[
v^2 = \frac{5000}{5} = 1000
\]

\[
v = \sqrt{1000} = 31.62 \, \text{m/s}
\]

So, the velocity of the mass is approximately **31.62 m/s**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does increasing mass affect kinetic energy if velocity is constant?
2. What happens to the kinetic energy if velocity doubles?
3. Can you calculate the velocity if the kinetic energy was doubled?
4. How much kinetic energy would a 20 kg mass have at 31.62 m/s?
5. What is the potential energy of the object if it was raised to a height of 10 meters?

**Tip**: Kinetic energy depends on the square of velocity, so even small changes in velocity significantly impact the kinetic energy.

Discover how to calculate the velocity of a 10 kg mass given 5kJ of kinetic energy using the formula KE = (1/2) mv^2. This physics problem involves algebraic manipulation and square root calculations, suitable for students in Grades 9-12.

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